45153

Автор(ы): 

Автор(ов): 

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Параметры публикации

Тип публикации: 

Статья в журнале/сборнике

Название: 

Algorithms of Inertial Mirror Descent in Convex Problems of Stochastic Optimization

Наименование источника: 

  • Automation and Remote Control

Обозначение и номер тома: 

Vol. 79, No. 1

Город: 

  • Москва

Издательство: 

  • Pleiades Publishing, Ltd

Год издания: 

2018

Страницы: 

78–88
Аннотация
A minimization problem for mathematical expectation of a convex loss function over given convex compact X ∈ R^N is treated. It is assumed that the oracle sequentially returns stochastic subgradients for loss function at current points with uniformly bounded second moment. The aim consists in modification of well-known mirror descent method proposed by A.S. Nemirovsky and D.B. Yudin in 1979 and having extended the standard gradient method. In the beginning, the idea of a new so-called method of Inertial Mirror Descent (IMD) on example of a deterministic optimization problem in R N with continuous time is demonstrated. Particularly, in Euclidean case the method of heavy ball is realized; it is noted that the new method no use additional point averaging. Further on, a discrete IMD algorithm is described; the upper bound on error over objective function (i.e., of the difference between current mean losses and their minimum) is proved.

Библиографическая ссылка: 

Назин А.В. Algorithms of Inertial Mirror Descent in Convex Problems of Stochastic Optimization // Automation and Remote Control. 2018. Vol. 79, No. 1. С. 78–88.

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